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World cup cephalopod fever

Submitted by kevin on Thu, 23/06/2011 - 12:59pm

World cup fever is again gripping the globe - well, perhaps not so strongly as last time, but the Women's World Cup football finals are about to begin in Germany. And as the excitement builds, the aquarium chain that brought us Paul the "psychic" octopus is rising to the new challenge. Paul himself has ascended to the great aquarium in the sky, so the search is on for a worthy successor

Each of the chain's eight aquariums in Germany has chosen its own octopus, and they will all be predicting the results of the matches involving Germany.

To be a spoilsport, though, even assuming our new cephalopod friends have no true predictive ability, there's a pretty good chance that some of them will still be looking as good as Paul after Germany's three matches in the group stages.

It's reasonable to take 3/8 as the probability that an octopus will make the right prediction by chance alone (allowing for the possibility of a draw in the group-stage matches). That means that there's a probability of about 0.35, that is, around one chance in three, that at least one of the eight creatures will predict the right result for all three of Germany's group-stage games. And it's very likely (95% chance) that the best octopus will get at least two out of the three games right, by chance alone.

We'll all have to wish for Germany to make it through to the quarter finals to give our octopus friends a real chance to show their psychic mettle (or more likely, show us more about how chance operates). And they don't have to knock England out to get that far - Germany and England are in different groups.

Germany's first group match, against Canada, is on Sunday 26 June, and the first octopus predictions are promised on Friday 24th. So we can all start getting excited! (Or perhaps not.)

It's all a publicity stunt for the aquaria, of course...
But in case people are still interested:
For the first Germany game, 3 of the octopuses predicted a win for Germany, 2 for Canada, and 3 predicted a draw.
Actual result was a 2:1 win for Germany.
Next German game is on Thursday 30th June, against Nigeria. England play today (Monday 27th) against Mexico.
Since it's now clear than the cephalopodic predictors can predict a draw, and indeed seem quite likely to do so, it's not clear that my assumption of a probability of 3/8 for a correct prediction is appropriate. Paul never predicted a draw, and the aquaria have changed the prediction task a bit. But, hey, I don't think I'll redo my calculations yet. One can push things too far...